Question

Two wires are as follows. The resistivities, lengths and radii are in the ratio $2:3$, $3:5$ and $2:7$ respectively. Their resistances are in the ratio of

• A. $49:10$
• B. $7:2$
• C. $2:4$
• D. $1:2$

Answer 1

Answer: (A)

$49:10$

$\frac{R_1}{R_2}=\left(\frac{{\rho }_1}{{\rho }_2}\right)\left(\frac{L_1}{L_2}\right)\left(\frac{A_2}{A_1}\right)$

$=\left(\frac{{\rho }_1}{{\rho }_2}\right)\left(\frac{L_1}{L_2}\right)\left(\frac{r_2^2}{r_1^2}\right)$

$=\frac{2}{3}\times \frac{3}{5}\times \left(\frac{2}{7}{)}^{-2}\right[\frac{r_2}{r_1}=\frac{7}{2}]$

$=\frac{2}{5}\times (\frac{4}{49}{)}^{-2}$

$=\frac{2}{5}\times \frac{49}{4}$

$\frac{R_1}{R_2}=\frac{49}{10}$